Speed and tangential velocity problem

Question

a 0.8kg pendulum bob hangs from the roof of a moving van. if the van is travelling 30m/s around a curve of 200m radius. find the angle which the cord makes with the vertical? solution please

Answer 1

The mass undergoes a centrifugal acceleration

a =v^2/r = 900/200 =9/2=4.5 m/s/s

The force that appears to push it HORIZONTALLY to the side is

F =ma = 0.8(4.5) = 3.6 N

The force of gravity that acts VERTICALLY downward is

W =mg = 0.8(9.8) =  7.84 N

These two forces are the sides of a force right triangle

The angle formed can be found by using the tangent function and the forces involved

tan(angle) = opposite force/adjacent force = horiz force/ vert force

tan(angle) = 3.6 N/ 7.84 N = 0.459183673

arctan( 0.459183673) =  24.7 degrees

Answer 2

m=0.8 kg

v=30 m/s

r=200 m

g=9.8 m/s^2

http://i299.photobucket.com/albums/mm286...

Centrifugal force: Fc=mv^2/r

F1=Fc*cosα=(mv^2/r)*cosα

Gravitational force: F=mg

F2=F*sinα=mg*sinα

F1=F2

(mv^2/r)*cosα=mg*sinα

tanα=v^2/rmg

α=atan(v^2/rmg)

α=29⁰51'